DETROIT (AP) _ Mazda Motor Corp. today unveiled a new luxury division that will sell cars under the Amati nameplate in the United States in three years.

The Amati, which Mazda officials said gets its name from a Latin word for ''to love,'' has yet to be priced. Richard Colliver, general manager of the Amati division, said the car would be competitive with the $20,000-$50,000 Toyota Lexus, Nissan Infiniti and Honda Acura.

Mazda plans to supply 50 dealers with two kinds of all-new sedans in 1994. The Amatis will be built at a new plant near Mazda's current assembly factory in Hofu, Japan.

Mazda's announcement comes during slumping auto sales and a recession that has hurt all automakers in the U.S. Through July, Mazda had sold 211,947 cars and trucks this year in the U.S., down 1 percent from the same period last year.

Clark Vitulli, senior vice president of Mazda Motor of America Inc., said things should be different when Amati cars cross the ocean.

''By the time our luxury cars come to market, the economic picture should be brighter,'' he said at a news conference. ''We believe the establishment of a second channel for us will strengthen our position.''

Mazda's luxury-car project has been discussed for years. The company already sells a luxury vehicle, the 929, in the United States.

The luxury market is going through a major transition. Sales of Japanese- made vehicles are increasing while sales of Big Three and European luxury cars are falling.

Much of the market is immune to recession simply because likely buyers already are wealthy. But, for companies marketing cars only in the luxury end, the segment can be treacherous.

Rover Group, for instance, decided earlier this month to stop selling its Sterling cars in the United States because it simply wasn't economically feasible.

Through the first seven months of this year, Japanese automakers' luxury- car sales were up 12 percent while Big Three sales were down 11 percent and European luxury-car sales are off 23 percent, according to Jacobs Automotive Inc. of Little Falls, N.J.

Honda Motor Co. Ltd. introduced its Acura division in 1986. That was followed in late 1989 by Toyota Motor Corp.'s Lexus division and Nissan Motor Co. Ltd.'s Infiniti division.

Through the first seven months of this year, Acura sales were running 25 percent ahead of last year, Lexus sales were up 2 percent and Infiniti sales, which got off to a slow start last year, were up 85 percent.

On the flip side, sales by Mercedes-Benz of Germany were down 22 percent, sales by Porsche of Germany were down 51 percent and sales of England's Jaguar cars were off 52 percent.

The European luxury cars have been clobbered by the federal luxury tax and a doubling of the gas-guzzler tax, both of which began Jan. 1.